Its sounds like an anti-cheat is seeing something wrong. Are you running any anti cheat programs? (Cheating-death or Paladin?) Also, when you log on to the server does it mention anything about scanning your hard drive for cheats? Some anti-cheat programs misidentify the OpenGl drivers. If that is the problem, you need to download a modded OpenGL driver set (Version 2.5 if I remember correctly) Heres the link for paladin anticheat, check there first as they KNOW theres a problem with ATI cards being detected incorrectly, and may have a solution. Also, try another server and let us know if you get a message that your HD is being scanned for cheats. You should be able to play in servers that dont use any anti cheat.
Paladin Anticheat
Try that first, if it doesnt work, PM me or post here. But, thats the only thing I can think of right off. Also, have you used ANY mods or cheats for EITHER Half Life OR CS? I belivee Paladin scans ALL Seiarra Half Life software (HL, TFC, CS....) So a cheat somewhere else may be interfereing, but chances are its a OpenGL driver as thats kinda a known issue....